Keep your options open. Since you mentioned it may take a few months before you take possession of the car, you have time to check several options.

The DeLorean Convention and Show has had DMC Midwest help restore two DeLoreans (for the DCS Raffle Cars) within the last 18 months.
The 2015 Raffle Car has put on over 5,000 miles since October 2015 and the 2016 Raffle Car put on over 1,000 "test miles" by July 22, 2016.

The 2016 Raffle Car was "revived" after being stored for the last 12 - 15 years (half of your storage) and the car needed plenty of attention.

DMC Midwest uses an enclosed trailer (via Gullwing Transport) for transporting, which I highly recommend for DeLoreans, whenever possible.

I know Mike schedules transports a few times a month and you can schedule your pick-up on a weekend, which can make things even easier.